Three minutes after I arrive at Passmores Academy, in the middle of an estate in Harlow, Essex, the fire alarm goes off. "Obviously this isn't ideal," says the headteacher, Vic Goddard, as we file out of the building, though I couldn't disagree more – I get to see the whole school, all 930 pupils and a good number of the 200 staff, quietly lining up on a football pitch. "You shouldn't be talking," a passing member of staff says to Graham, the Guardian's photographer, and me. We have been told off for talking! At school! What a thrill.

False alarm over, the students quietly walk back to the building. Goddard, who must be over 6ft 3in, towers over his students. "Sir, is there a fire?" asks a tiny worried-looking boy. "No, a science experiment set off the smoke alarm," Goddard tells him. Another boy, even more worried: "Sir, does this eat into our break time?" "I'll make sure it doesn't."

What is most noticeable about these students is the warmth of their relationship with their headteacher. They are not intimidated by him; there is no distance between them. When Goddard is having his photograph taken, one kid says: "Bet you love having your photograph taken, don't you, Sir" and Goddard fires back: "Not since I grew these extra chins – I used to be thin and handsome once, but ex-PE teachers tend to widen" and the boy beams.

We walk back to his office – Goddard smoothly responding to every "hi, Sir", telling one boy to tuck his collar in, asking another if he'd got his football boots sorted out – and I get the impression life was like this even before reality television fame.

In Educating Essex, the fly-on-the-wall series filmed in his school, Goddard and Stephen Drew – the deputy headteacher, or to give him his proper title, according to one pupil in the first episode, "evil overlord" – are the clear stars. To begin with, Channel 4 filmed some of the pupils going to parties and hanging around with their friends, but it became clear that the most interesting viewing was to be found at school. "We deal with every extreme of human behaviour," says Goddard.

Despite its rather cynical title – clearly hoping to attach itself to the Only Way is Essex bandwagon – it is a touching, insightful look at secondary-school life. Both Goddard and Drew claim to be amazed at its reception so far. "I honestly thought only Harlow and my mum would watch it," says Goddard. He received 2,500 emails in the 24 hours after the first episode, "and only two were negative. So it was the right decision [to take part], even with what's happened over the last few days."

I hadn't expected how deeply a bit of criticism of the school – and its teachers – would hit Goddard and Drew, but it's a subject they keep returning to. The tabloids picked up on one of the teachers saying to his class at the end of a lesson, "Clear off scumbags" and criticised Drew for calling the headteacher a "bugger" (in one of the show's funniest scenes, Goddard hid behind a door and jumped out to surprise his deputy). "A lot of what has been said misses the whole thing about relationships," says Drew.

"We are who we are and you can't hide it when they're filming for 12 months," says Goddard. He was so stung by some of the stories in the papers that he used the school assembly on Monday to address it. "I said: 'Yes, you did see me step out from behind the door and stick my fingers up at Mr Drew. If you were offended, I apologise, but actually he's my mate and we have a very good relationship.'" Students have asked him how he can justify excluding them from school for swearing now. "I say: 'You're right, but swearing isn't the key thing here – it's the lack of respect that comes with the use of that word, the lack of understanding of the context when you swear at somebody.' My staff don't turn up to be sworn at. So if a kid swears at Stephen, I exclude them. That's the only thing they've come back to me with."

Drew insists that pupils watching him in more private moments – eating cereal at his desk while singing along to Fairytale of New York one morning last winter, for instance – doesn't undermine his authority. "It's really funny when people say that because that suggests somehow that's not what the kids see anyway. If kids see you as human their respect for you will increase. People who argue that it breaks down the barriers show their lack of understanding of the ways you have to be when you are working with young people."

Drew knows people have criticised the staff for being "too matey" but says: "Kids coming through that door at the start of Year 7 are with you for five years. OK, I'll shout and scream at you for the first thing you do wrong, destroy you, punish you to the end of the earth and you will hate me. Great, I've proved a point – I'm in charge. Brilliant. Next time I have to deal with you and help you through something, you're not going to trust me. Whereas if we can have a bit of a laugh, a bit of a positive relationship, that's much better. You're still dealing with them but it's in a much more fluid way and so much more effective."

Goddard breaks in: "That whole perception that we're friends with the children … I don't go out and socialise with them! They're not the people I spend my weekends with. But I like them, and why shouldn't they know that we like them, that when they turn up we're pleased to see them?"

Ofsted judged Passmores "outstanding" in 2008, the highest rating. This term, it became an academy and moved into a new building. Goddard estimates that between 30 and 40% of its pupils are eligible for a free school meal, yet only around half take it up. The school has a higher than average proportion of children with special educational needs, and a 50% A*-C GCSE pass rate including English and maths, slightly below the national average but it is improving and Goddard points out they have beaten the local authority's targets every year for the last five years. There are, he says, "challenges" (never, I notice, "problems"). In the first episode one pupil, Carmelita, is excluded after swearing at Mr Drew and she then makes a (false) allegation of assault against him. Other episodes feature teen pregnancy, bullying and one pupil being taken into care. It raises obvious questions about how – and if – vulnerable children should be exposed on television. "The biggest and first concern was how the children would be protected," says Goddard. "They have been incredibly well looked after by the production team. They have seen every second of footage with their families. They've had the child psychologist report. Carmelita has been a very difficult young lady, but her feedback has been interesting after seeing herself through someone else's eyes; to sit and watch that has been such a learning experience for her."

The biggest challenge, says Goddard, "is what the outside world does to our children. What society inflicts on them on a daily basis. I will pick up a kid for not having their top button done up or their shirt tucked in and that child will be going home to no food, no mum or dad in. I went to a house once with no running water. That is their reality, so us asking them to do their tie up, yes, we are crazy, that is a stupid thing to ask in light of that, but it also teaches them that their background shouldn't affect their future."

The presence of mobile phones and the internet is a constant problem because "kids want instant answers when actually you want them to love the learning process," says Goddard. He runs a "no-fail" organisation, he says. "If a student doesn't get the results they need to move on, we've failed. I don't want, next summer, my students or my ex-students on the street rioting. If we kick them out, if we say: 'You're too difficult,' who makes sure their journey goes in the right direction if we don't? Parents, you'd hope, but they're not necessarily reliable. Our job is to make sure they have positive choices to make. It's very easy to blame society's ills on teachers but our kids spend six hours out of their 24 here."

"I have this real feeling that as a society we are grotesquely unfair to young people," says Drew. "On the one hand, we want them to be these incredibly responsible people who understand everything and behave in a perfect way. We expose them to everything as if they are adults and I just think that parents, society, everyone, needs to take a step back and say: 'You know what? There's an 18 certificate on that DVD for a reason and you are 12 and no, you can't watch it. And I am going to find out how to make sure your privacy settings on your Facebook account are set properly because if I don't as a parent and I ignore it, I'm letting you down.' As a society we are too quick to say: 'They're kids, they'll work it out.' As adults, we need to take more responsibility."

It is too easy to vilify young people, he says. "People live in this total fantasy world about how somehow it was better in the past. It wasn't better at all – kids got beaten up, stabbed, kids smoked. It's just so much easier to see them now because they're posting their names and everything about themselves on Facebook because they don't think. And they put ridiculous photos online." He shakes his head. "But they're young."

What makes this school work? Undoubtedly it's the dedication of its staff (and the number; Goddard says he spends more than 90% of the school's budget on staff – an unusually high proportion). He works 14 hours a day, often six days a week; he says Drew works even harder.

"It is tiring, but every day these children deserve the same energy I've got," says Goddard. "This year's Year 11 deserve as much as we gave last year's Year 11." They are clearly driven by an evangelical zeal for this school, and for education, but surely you can't expect teachers to work like this. Both look blank for a second.

"You go into any school," says Drew, "and there are people doing what Vic and I do and probably doing it better, all over the country."

League tables don't bother Goddard "because that holds me publicly accountable and I should be". Free schools do bother him, but only because he thinks they shouldn't be necessary. "Every state school should be good enough to send every child to." Neither would work in a public school. "I wouldn't find it interesting," says Drew. "This interests me."

Goddard, particularly, is driven by the education he received at his south London comprehensive. "My eldest brother was the first boy to go to university from the school. My second brother was the second to go to university." Both his brothers, and his sister, are teachers. "Taking a council estate kid and giving him opportunities – it was about payback for me. I love my job and if that comes across in any way [in Educating Essex] and it helps someone else go into the best job in the world, then great."

Drew says he "just absolutely loves it. It's the constant contact with people, and the feeling you can make a difference. Young people are so energetic and vital in what they do. We don't do anything extraordinary. We turn up every day and teach with everything we've got and so does every teacher in the country."

The bell goes. Our lesson is over. It has been hard to get a word in between them and I feel a little dazed – bludgeoned, even – by the enthusiasm of Mr Drew and Mr Goddard, but inspired and heartened too. That was after an hour. Imagine what five years of it would do.